# Quasi-projective scheme

From Encyclopedia of Mathematics

A locally closed subscheme of a projective space . In other words, a quasi-projective scheme is an open subscheme of a projective scheme. A scheme over a field is quasi-projective if and only if there exists on an invertible ample sheaf. A generalization of the notion of a "quasi-projective scheme" is that of a quasi-projective morphism, that is, a morphism of schemes that is the composite of an open imbedding and a projective morphism. A scheme that is both quasi-projective and complete is projective.

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[a1] | R. Hartshorne, "Algebraic geometry" , Springer (1977) pp. 10; 103 MR0463157 Zbl 0367.14001 |

**How to Cite This Entry:**

Quasi-projective scheme.

*Encyclopedia of Mathematics.*URL: http://www.encyclopediaofmath.org/index.php?title=Quasi-projective_scheme&oldid=23946

This article was adapted from an original article by V.I. Danilov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article